@article{Watanabe2024, 
author = {Keiichi Watanabe},
title = {The Helmholtz decomposition of vector fields for two-dimensional exterior Lipschitz domains},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {7},
pages = {17886-17900},
keywords = {exterior Lipschitz domains, Helmholtz decomposition},
url = {https://www.sciopen.com/article/10.3934/math.2024870},
doi = {10.3934/math.2024870},
abstract = {Let    Ω be an exterior Lipschitz domain in              R        2  . It is proved that the Helmholtz decomposition of the vector fields in        L    p    (  Ω  ;            R        2    ) exists if    p satisfies    |  1      /    p  −  1      /    2  |  <  1      /    4  +  ε with some constant    ε  =  ε  (  Ω  )  ∈  (  0  ,  1      /    4  ], where it is allowed to take    ε  =  1      /    4 if    ∂  Ω  ∈      C    1  .}
}